The field of the invention is systems and methods for medical image reconstruction. More particularly, the invention relates to systems and method for simultaneously reducing image artifacts while reconstructing images from data obtained with a medical imaging system, such as an x-ray computed tomography system.
With conventional image reconstruction techniques, such as filtered backprojection for x-ray CT imaging and Fourier-based reconstructions techniques for MRI, a single image is reconstructed from a corresponding set of data acquired with the medical imaging system. For example, one image is reconstructed from a single sinogram in x-ray CT imaging and one image is reconstructed from one k-space data set in MRI. This correspondence between data and the images reconstructed from that data is because these traditional image reconstruction techniques are based on the assumption that all of the acquired data are consistent with each other. Routinely, however, data acquired with medical imaging systems are not consistent with a single true image of the subject being imaged, or a single state of a true image object that has dynamic characteristics.
These inconsistencies manifest as artifacts in the reconstructed images and can have many different origins. For example, in x-ray CT imaging, artifacts can result from the presence of metal objects in the subject, by acquiring too few projections, from beam-hardening effects, from x-ray scattering, subject motion, and so on. In MRI, artifacts can result from undersampling k-space, magnetic field inhomogeneities, subject motion, and so on. Inconsistencies between the acquired data and the stationary state of a true image of the subject can also have other sources, such as the presence of an exogenous contrast agent that if administered to the subject and the travels through the subject's vasculature. The assumption that the reconstructed image should be consistent with the acquired data is embodied in the following imaging model:AI=Y  (1);
which states that image reconstruction techniques should seek to reconstruct an image, I, that when forward projected is consistent with the acquired data, Y. The matrix, A, is referred to as the system matrix, which can be generally regarded as a forward projection operator that relates the reconstructed image, I, to the acquired data samples, Y. Eqn. (1) imposed that the reconstructed image, I, must be consistent with the measured data samples, Y; thus, Eqn. (1) can also be referred to as the “data consistency condition.” In x-ray CT imaging, the system matrix can include a reprojection operation and in MRI the system matrix can include a Fourier transform operation. The consistency condition of Eqn. (1) put in other words, states that when an image is faithfully reconstructed, the forward projection of that image should be substantially similar to, or consistent with, the data actually acquired with the imaging system.
To reconstruct an image, I, from the measured data, Y, it is often required that the data satisfy the so-called data sufficiency condition, which is a condition that allows for an inverse reconstruction formula to be used to reconstruct the image from the measured data. In x-ray CT imaging, the data sufficiency condition is the so-called Tuy condition, which requires the data samples to be acquired in an extended angular range around the image object. In MRI, the data sufficiency condition is the complete population of the entire Fourier space. Even when the data sufficiency condition is satisfied, however, still another condition needs to be met to reconstruct a true image of the image object. The discretely acquired data samples also need to satisfy the associated sampling criterion for a given reconstruction scheme.
Examples of data sampling criteria include the view angle sampling requirement in x-ray CT and the Nyquist sampling criterion in MRI. When the data sampling criterion is met in x-ray CT, filtered backprojection can be used to reconstruct an image, and when the data sampling criterion is met in MRI, Fourier inversion can be used to reconstruct an image. When an iterative image reconstruction method is employed, the data sampling criteria are often significantly relaxed. One example of such a method is compressed sensing based iterative image reconstruction techniques.
In an ideal situation, when the aforementioned data sufficiency condition and data sampling conditions are satisfied, an artifact-free image can be reconstructed. This ideal situation is impractical in the real world, however, due to complications of data acquisition conditions and complications from the objects being imaged. As a result of these complications, the acquired data may not represent the same physical state of the image object, or may not be acquired under the same physical conditions. Thus, the acquired data are referred to as “inconsistent data.” The physical reasons for these inconsistencies, whether because of a non-ideal acquisition system or because of a change in the physical state of the object during data acquisition, are referred to as the sources of inconsistency.
When the acquired data are no longer consistent due to sources of inconsistency, such as those described above, the consistency condition begins to break down. That is, the acquired data are no longer consistent when physical effects such as subject motion, contrast enhancement, noise, beam hardening in x-ray imaging, and so on are present during the data acquisition process. The inconsistencies in the acquired data manifest as artifacts in the reconstructed images.
It would therefore be desirable to provide systems and methods for reconstructing a medical image from data acquired from a medical imaging system that account for the level of inconsistencies in the acquired data, such that a faithful representation of the true image of an imaged subject can be produced.